Exposure apparatus and method of manufacturing device

ABSTRACT

An exposure apparatus the present invention comprises: an illumination optical system configured to illuminate an illumination area on an original with light from a light source; a projection optical system configured to project a pattern of the original onto a substrate; a first stage configured to hold the original; a second stage configured to hold the substrate; and a controller configured to control driving of at least one of the first stage, the second stage, and an optical element which forms the projection optical system so as to reduce variations in imaging characteristics of the projection optical system, based on a dependence of a transmittance of the pattern on a position in the illumination area.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an exposure apparatus in whichvariations in imaging characteristics are reduced.

2. Description of the Related Art

A process of manufacturing a semiconductor device such as an LSI or VLSIformed from an extra fine pattern has conventionally adopted a reductionprojection exposure apparatus which reduces and prints by exposing acircuit pattern drawn on a mask on a substrate (also called a “wafer”)coated with a photosensitive agent, thereby forming a desired pattern onthe substrate. Along with an improvement in the packaging density ofsemiconductor devices, further micropatterning is becoming necessary. Ademand for micropatterning on the exposure apparatus is increasing alongwith the development of the resist process.

To improve the resolving power of an exposure apparatus, there are amethod of shortening the exposure light wavelength and a method ofincreasing the numerical aperture (NA) of a reduction projection lens.As the resolving power increases, the depth of focus of the reductionprojection lens decreases. It is therefore important to improve thefocus accuracy of focusing the wafer surface on the imaging plane (focalplane) of the reduction projection lens. One important opticalcharacteristic of the projection exposure apparatus is the alignmentaccuracy of precisely aligning various patterns obtained by a pluralityof processes. An important factor which influences the alignmentaccuracy is a magnification error of the reduction projection lens.Along with a stronger trend toward further micropatterning of a VLSIevery year, a need for improving the alignment accuracy is becomingstronger. It is therefore very important to maintain the magnificationof the reduction projection lens at a predetermined value.

A reduction projection lens is known to partially absorb exposure energyso that the temperature of the reduction projection lens changes due toheat generated by the absorption, leading to a change in the opticalcharacteristics of the reduction projection lens, such as the refractiveindex. When the reduction projection lens is continuously irradiatedwith exposure light for a long period of time, the imagingcharacteristics (including at least one of the focus, magnification, andwavefront aberrations such as astigmatism aberration and distortionaberration) of the reduction projection lens vary. This may result innon-negligible amounts of focus errors or alignment errors. Under thecircumstance, there is proposed a method of correcting variations inimaging characteristics, which occur when exposure energy is applied tothe reduction projection lens.

For example, the applicant of Japanese Patent Publication No. 63-16725proposes calculating the amounts of variations in imagingcharacteristics, which occur when exposure energy is applied to thereduction projection lens by model equations using, e.g., the exposureamount, exposure time, and non-exposure time as variables. Based on thecalculation result, the variations in imaging characteristics of theprojection optical system are corrected. The model equations haveimaging characteristic-specific coefficients unique to the reductionprojection lens. Measuring the coefficients makes it possible to correctthe variations in the imaging characteristics of the reductionprojection lens.

There is also proposed an exposure apparatus which can obtain a moreexcellent projection resolving power for a specific pattern by changingthe illumination shape. In such an apparatus, a light sourcedistribution generated on the pupil surface of the reduction projectionlens changes depending on the exposure conditions (e.g., the numericalaperture of a projection system, the numerical aperture of anillumination system, the exposure area, the exposure center position,and the exposure mask). Therefore, the variation amounts of imagingcharacteristics change for the respective exposure conditions.

Under the circumstance, there is proposed an exposure method ofsatisfactorily adjusting the variations in imaging characteristics evenwhen the distribution of energy applied to the reduction projection lenschanges. For example, Japanese Patent No. 2828226 proposes a method ofstoring imaging characteristic correction coefficients corresponding tovarious states of the illumination light source distribution, andreading out corresponding correction information when the state of thelight source distribution is changed, performing correction based on thereadout information. To precisely correct variations in imagingcharacteristics corresponding to various states of the illuminationlight source distribution, it is necessary to calculate a correctioncoefficient best suited to a set of exposure conditions of interest frompieces of information on, e.g., the state of the illumination lightsource distribution on the pupil plane, the reticle transmittance, thedimensions of the exposure area in the scanning direction and in adirection perpendicular to the scanning direction, the scanning speed,the exposure amount, and the irradiation time.

It is necessary to calculate a correction coefficient best suited to aset of exposure conditions of interest. For this purpose, thetransmittance of a mask needs to be calculated from mask transmittanceinformation (e.g., mask transmittance map information/mask designinformation) and information on the exposure area on the mask. However,the prior arts do not take account of the difference in transmittance(the difference in pattern density) attributed to the image height inthe illumination area. Still worse, even when the pattern density in theillumination area is calculated from the mask transmittance informationand illumination area information, correction systems in the prior artshave poor correction capabilities.

Nowadays, however, the correction systems are being upgraded to meet ademand for an improvement in the accuracy of the exposure apparatus.This has made it possible to correct variations in imagingcharacteristics which depend on the image height in the illuminationarea.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an exposureapparatus in which variations in imaging characteristics attributed tothe dependence of the transmittance of a pattern formed on a mask on theposition in the illumination area are reduced.

According to the present invention, there is provided an exposureapparatus comprising an illumination optical system configured toilluminate an illumination area on an original with light from a lightsource; a projection optical system configured to project a pattern ofthe original onto a substrate; a first stage configured to hold theoriginal; a second stage configured to hold the substrate; and acontroller configured to control driving of at least one of the firststage, the second stage, and an optical element which forms theprojection optical system so as to reduce variations in imagingcharacteristics of the projection optical system, based on a dependenceof a transmittance of the pattern on a position in the illuminationarea.

Further features of the present invention will become apparent from thefollowing description of exemplary embodiments with reference to theattached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view showing an exposure apparatus according to anembodiment of the present invention;

FIG. 2 is a graph showing the irradiation variation characteristic ofthe aberration of a reduction projection lens;

FIG. 3 is a view showing an example of the mask pattern layout;

FIG. 4 is a view showing the relationship between the exposure area on amask and the irradiation area of a projection optical system;

FIG. 5 is a flowchart illustrating how to calculate a correctioncoefficient;

FIG. 6 is a view showing the light intensity distribution on the pupilplane;

FIG. 7 is a table showing a mask transmittance map;

FIG. 8 is a view showing divided illumination areas;

FIG. 9 is a table showing an approach to calculating the masktransmittances in the divided illumination areas;

FIG. 10 is a table showing normalized mask transmittances in the dividedillumination areas;

FIG. 11 is a table showing an approach to calculating a weightingcoefficient from the divided illumination areas;

FIG. 12 is a table showing an exposure time weighting method;

FIG. 13 is a graph showing the relationship between the image height andthe amount of aberration variation;

FIG. 14 is a flowchart illustrating exposure processing;

FIG. 15 is a graph showing an example of a correction positioncalculation method;

FIG. 16 is a graph showing another example of the correction positioncalculation method;

FIG. 17 is a plan view and a sectional view showing driving mechanismsof a projection system; and

FIG. 18 is a view showing the transmittance map image height andaberration correction equation.

DESCRIPTION OF THE EMBODIMENTS

Variations in imaging characteristics in an exposure apparatus accordingto embodiments of the present invention include a variation in at leastone of the focus, magnification aberration, distortion aberration,astigmatism aberration, spherical aberration, coma aberration, and otherwavefront aberrations. As is well known in the technical field of thepresent invention, the wavefront aberrations are expressed as therespective terms of an expression obtained by expanding the wavefrontshape using the Zernike polynomial. These wavefront aberrations are alsocollectively called “aberration”.

First Embodiment

FIG. 1 shows the schematic arrangement of a scanning exposure apparatusaccording to an embodiment of the present invention. A pulse lasersource 101 contains, e.g., ArF gas and emits a laser beam with afar-ultraviolet wavelength of 193 nm. The pulse laser source 101includes, e.g., a front mirror which constitutes a resonator, awavelength range narrowing module which includes, e.g., a diffractiongrating and prism and narrows the exposure wavelength range, a monitormodule which includes, e.g., a spectroscope and detector and monitorsthe wavelength stability and spectral width, and a shutter.

A laser controller 102 performs, e.g., the control of gas exchange,wavelength stabilization, and a discharge voltage in the pulse lasersource 101. In this embodiment, the control is not performed by thelaser controller 102 alone and can be performed in accordance with aninstruction from a main controller 103 for the overall exposureapparatus, which is connected to the laser controller 102 via aninterface cable.

The beam emitted by the pulse laser source 101 is shaped into a desiredbeam shape via a beam shaping optical system of an illumination opticalsystem 104, enters an optical integrator, and forms a large number ofsecondary sources to illuminate a mask 109 with a uniform illuminancedistribution.

An aperture stop 105 of an illumination system has a nearly circularaperture so that an illumination system controller 108 can set theaperture diameter of the aperture stop 105 and, eventually, thenumerical aperture of the illumination optical system 104 to desiredvalues. Since the ratio of the numerical aperture of the illuminationoptical system 104 to that of a projection optical system 110 is thecoherence factor (σ value), the illumination system controller 108 canset the σ value by controlling the aperture stop 105 of the illuminationsystem.

A half mirror 106 is inserted into the optical path of the illuminationoptical system 104. A certain component of exposure light, whichilluminates the mask 109, is reflected and extracted by the half mirror106. An ultraviolet photosensor 107 is inserted in the optical path ofthe light component reflected by the half mirror 106, and generates anoutput corresponding to the intensity (exposure energy) of the exposurelight.

The output from the photosensor 107 is converted into exposure energyper pulse by an integration circuit (not shown) which performsintegration for each pulse emission of the pulse laser source 101. Theconverted exposure energy is input to the main controller 103 whichcontrols the overall exposure apparatus via the illumination systemcontroller 108.

The circuit pattern of a semiconductor device to be printed is formed onthe mask (reticle) 109 serving as an original. The illumination opticalsystem 104 irradiates the illumination area (exposure slit) on the mask109 with a laser beam. The mask 109 is held by a mask stage (not shown).The mask stage moves the mask 109 to scan the mask 109 with a laser beam(illumination area), thereby exposing the exposure area on the mask 109.The projection optical system 110 is set so as to reduce the circuitpattern image of the mask 109 at a reduction magnification β (β is,e.g., ¼) and image and project the reduced image onto a wafer 115serving as a photosensitive substrate coated with a photoresist. Thepattern formed on the mask 109 is transferred onto the wafer 115 servingas a substrate via the projection optical system 110. An aperture stop111 of the projection optical system 110 has a nearly circular apertureand is inserted on the pupil plane (the Fourier transformation planewith respect to the reticle) of the projection optical system 110. Bycontrolling the aperture diameter of the aperture stop 111 using adriver 112 such as a motor, the numerical aperture of the aperture stop111 can be set to a desired value.

A field lens driver 113 moves a field as a constituent element of a lenssystem in the projection optical system 110 onto the optical axis of areduction projection lens using, e.g., the air pressure or apiezoelectric element, so that deterioration in various aberrations ofthe reduction projection lens is prevented and a satisfactory projectionmagnitude is ensured, thus reducing distortion errors. A projection lenscontroller 114 controls optical elements of the projection opticalsystem 110.

A wafer stage 116 serving as a second stage which holds a substrate canthree-dimensionally move along the optical axis direction (Z direction)of the projection optical system 110 and on a plane (X-Y plane)perpendicular to this direction. A laser interferometer 118 measures thedistance between the wafer stage 116 and a movable mirror 117 fixed toit, thereby detecting the position of the wafer stage 116 on the X-Yplane. A stage controller 120 under the control of the main controller103 of the exposure apparatus detects the position of the wafer stage116 by the laser interferometer 118 and controls a driver 119 such as amotor to move the wafer stage 116 to a predetermined position on the X-Yplane. A mask stage controller, the stage controller 120, the projectionlens controller 114, and the main controller 103 constitute a controllerwhich controls the driving of the optical elements of the projectionoptical system, the first stage which holds the mask, and the secondstage which holds the substrate.

A light-projecting optical system 121 and detection optical system 122constitute a focal plane detector. The light-projecting optical system121 projects a plurality of light beams formed from non-exposure lightwhich does not expose the photoresist on the wafer 115. The light beamsare converged on the wafer 115 and reflected by it. The light beamsreflected by the wafer 115 enter the detection optical system 122.Although not shown, a plurality of position detection light-receivingelements are inserted in the detection optical system 122 incorrespondence with the respective reflected light beams. Thelight-receiving surface of each position detection light-receivingelement is set nearly conjugate to a corresponding light beam reflectionpoint on the wafer 115 by an imaging optical system. A positional shiftof the surface of the wafer 115 in the optical axis direction of theprojection optical system 110 is measured as a positional shift of theincident light beam on the position detection light-receiving element inthe detection optical system 122.

Model equations of a variation in the aberration of the projectionoptical system 110 upon exposure energy irradiation, and a correctioncoefficient used to quantize the model equations according to thisembodiment will be explained.

FIG. 2 shows an example of a temporal change in the aberration of theprojection optical system by exposure. The abscissa indicates a time t,and the ordinate indicates an aberration variation amount ΔF at acertain image height of the projection optical system 110. Theaberration herein means, e.g., the focus, magnification, distortion,astigmatism aberration, spherical aberration, and coma aberration. Theaberration variation amount ΔF generally takes an image height-specificvalue. The initial amount of aberration of the projection optical system110 is indicated by F0. As the projection optical system 110 startsexposure upon receiving exposure light from the pulse laser source 101at time t0, the amount of aberration varies with time and becomes stableupon reaching a predetermined amount of aberration F1 at time t1. Afterthat, even when the exposure light is continuously applied to theprojection optical system 110, the amount of aberration does not changefrom F1 because energy which transforms into heat upon being absorbed bythe projection optical system 110 equilibrates with thermal energydischarged by the projection optical system 110. As the exposure isstopped at time t2, the amount of aberration returns to the originalstate with time and reaches the initial amount of aberration F0 at timet3.

Time constants TS1 and TS2 in FIG. 2 are equivalent to those of the heattransfer characteristic of the projection optical system 110. Sincethese time constants are aberration-specific values unique to theprojection optical system 110, they are acquired for each apparatus andaberration in inspecting the projection optical system 110.

A method of calculating the maximum amount of aberration variation F1 inFIG. 2 will be explained. The maximum amount of aberration variation F1can be expressed by:

F1=K×Q   (1)

where K is the amount of aberration variation per unit amount of light(unit exposure energy) as a correction coefficient, and Q is a valuecalculated from the parameters of conditions (e.g., information on theexposure amount, scanning speed, and exposure area) which determineactual exposure energy.

Let ΔF_(k) be the amount of aberration at a certain time. Then, usingthe maximum amount of variation F1 and the time constants TS1 and TS2stored for each aberration, an amount of aberrationΔF_(k+1) afterexposure for only a time period At from the certain time ΔF_(k) isapproximated by:

ΔF _(k+1) =ΔF _(k) +F1×(1−exp(−Δt/TS1))   (2)

Likewise, an amount of aberrationΔF_(k+1) when exposure is not performedfor the time period Δt from the certain time ΔF_(k) is approximated by:

ΔF _(k+1) =ΔF _(k)×exp(−Δt/TS2)   (3)

A curve indicating the irradiation variation characteristic of theaberration of the projection optical system 110 shown in FIG. 2 ismodeled by the functions in equations (2) and (3) to predict a variationin the aberration of the projection optical system due to the generationof exposure heat. Note that the modeling functions in equations (1),(2), and (3) are merely an example, and the curve may be modeled usingother equations.

A correction coefficient K necessary for correcting a variation inimaging characteristic, which occurs upon exposure in accordance withthe illumination area and the dependence of the pattern transmittance onthe position in it, needs to be calculated for each exposure condition.This is because when the exposure conditions change, the energy densitydistribution of light which enters the projection optical system 110changes, resulting in changes in the amount of aberration variation ofthe projection optical system and in its dependence on the image height.The exposure conditions herein mean the effective light source shape,the mask pattern, and the exposure area on the mask.

In order to calculate a correction coefficient corresponding to theenergy distribution of light which enters the projection optical system,a first process of calculating and storing a correction coefficient forpredicting a variation in the aberration of the projection opticalsystem by taking account of the illumination area on the mask and thedependence of the pattern transmittance on the position in it will beexplained.

As shown in FIG. 3, an exposure pattern is laid out on the mask. Thepattern layout is generally nonuniform in the entire mask area, and thepattern density, i.e., pattern transmittance has a deviation. For thisreason, even if the energy distribution of irradiation light is uniformover the entire mask surface, the energy distribution of a lightcomponent transmitted through the pattern is nonuniform. This deviationin the energy distribution is averaged by scanning in the scanningdirection (in this case, the Y direction), but it remains in a direction(in this case, the X direction) perpendicular to the scanning directionas a difference in image height of the energy distribution.

As shown in FIG. 4, there is a case in which the mask is partiallyshielded by a light-shielding member so that exposure is performed bylimiting the mask exposure area. In this case, a difference in imageheight of the energy distribution is influenced by a mask rangedetermined as the exposure area.

In this embodiment, a method of calculating a correction coefficient bytaking account of the pattern transmittance distribution andillumination area will be explained. FIG. 5 illustrates a correctioncoefficient calculation sequence. A first calculator of the maincontroller 103 performs the correction coefficient calculation.

In step 1, the first calculator writes information of the exposureconditions to a memory. The pieces of the information are the type of anexposure mask, the illumination area, and the effective light sourceshape. The effective light source shape information is obtained inadvance based on the measurement result and/or the simulation resultobtained by a computer. For example, as shown in FIG. 6, the pupil planeis divided into 101×101 areas so that a pupil plane light intensity mapgenerated by normalizing the light intensity in each area by a maximumlight intensity is used as the effective light source shape information.

In step 2, the first calculator reads out exposure mask transmittanceinformation (to be referred to as a mask transmittance map hereinafter)as shown in FIG. 7. This information is light amount data in a matrix,which is obtained by measuring the amounts of light of a projected imageon the entire mask surface under appropriate measurement conditions. Theapparatus measures and stores the mask transmittance map for each mask.Although the mask transmittance map uses matrix data defined by 8 datapoints in the X direction and 10 data points in the Y direction in thisembodiment, the amounts of light may be acquired at an arbitrary numberof data points in an arbitrary area. Also, although a mask transmittancemap generated by the exposure apparatus is used in this embodiment, themask transmittance may be calculated based on, e.g., mask designinformation (e.g., CAD information). When the mask transmittance mapinformation or mask design information is used by a plurality ofexposure apparatuses, the information may be stored in a server whichallows a plurality of exposure apparatuses to commonly use it.

In step 3, as the first calculation processing procedure, the firstcalculator divides the illumination area into a plurality of areas inthe X direction, and individually calculates the mask transmittances inthe respective divided areas. In this embodiment, the dimension of theillumination area in the X direction is 26 mm (a value when convertingthe dimension of the illumination area in the X direction on the maskinto that on the wafer). Although this embodiment will exemplify a casein which the illumination area is divided into 8 areas with equal areasas shown in FIG. 8, the number of divided areas may be an arbitrary oneof 2 or more. The divided areas are obtained by dividing the rangewithin which the exposure light enters the projection optical systeminto a plurality of areas. As shown in FIG. 9, the mask transmittance inthe divided area (to be referred to as divided area n; n is the areanumber that is one of 1 to 8 in this embodiment) is calculated as theaverage of transmittance data in a mask area scanned along division arean by:

(the mask transmittance in divided area n)=(Σ transmittance data)/(thenumber of data points)

(Note that the Σ range is defined as only a mask area scanned alongdivided area n)

In step 4, the first calculator normalizes the mask transmittance individed area n, and calculates a mask transmittance r_(n) in eachdivided area, as shown in FIG. 10.

In steps 5 and 6, the first calculator calculates an exposure area ratiog_(n) of divided area n based on exposure area information. The exposurearea information herein includes a dimension w of the exposure area inthe X direction, and an X-image height x₀ at the center of the exposurearea. These pieces of information can be substituted by X-coordinates xrand x1 at the two ends of the exposure area. The dimension of theexposure area in the Y direction is taken into consideration as thescanning distance not herein but in a calculation process to bedescribed later.

The g_(n) value is given as the area ratio between divided area n and aportion in divided area n, which is included in the illumination areaunder a certain set of exposure conditions. That is, the g_(n) value canbe calculated on a case-by-case basis as follows:

A case in which divided area n is included in the illumination area:g_(n)=1

A case in which divided area n is not included in the illumination area:g_(n)=0

A case in which divided area n is partially included in the illuminationarea: g_(n)=((the ratio of a portion in divided area n, which isincluded in the illumination area)/(the area of divided area n)) FIG. 11shows a detailed example of the calculation result.

In step 7, the first calculator calculates the weighting coefficientfrom the mask transmittance information and exposure area information.Let λ_(n) be the weighting coefficient calculated by multiplying ther_(n) value calculated from the mask transmittance by the g_(n) valuecalculated from the exposure area information. Then, the coefficientλ_(n) corresponds to a value obtained by normalizing the amount of lightenergy which propagates through divided area n.

Steps 3 to 7 are repeated for each divided area n (eight times in thisembodiment), and the weighting coefficient An in each divided area n iscalculated and stored.

Using the calculated weighting coefficient λ_(n) for each divided area,an aberration function:

f_(n) ^(I,C)(x)   (1)

is weighted, where n is the divided area number, I is the effectivelight source shape on the pupil plane, C is the type of aberration, andx is an arbitrary X-image height. Expression (1) represents the degreeof influence of the mask transmittance and exposure area on theaberration C as an imaging characteristic, which is generated by theprojection optical system when divided area n is exposed with theeffective light source shape I by the unit exposure amount, as afunction of the image height x. That is, the aberration function meansthe degree of influence, on the imaging characteristic, of the masktransmittance and exposure area determined for each of the plurality ofareas obtained by dividing the range within which the exposure lightenters the projection optical system. The image height x is notparticularly limited to image heights inside the divided area n. Thismeans that the light which enters the divided area n can change theaberration not only at image heights inside the divided area n but alsoat image heights outside the divided area n. The aberration function andits coefficients generally differ for each aberration C, e.g., afunction for focus is not necessarily equal to one for image shift. Ingeneral, the coefficients also differ for each effective light sourceshape I. In this embodiment, an appropriate function is selected basedon the effective light source information read out in step 1. Thedependence of the aberration on the image height only in the X directionis expressed as a function in this embodiment. However, when thedependence of the aberration on the image height in the Y directionneeds to be taken into consideration in aberration correction to bedescribed hereinafter, the aberration function may be expanded into:

f_(n) ^(I,C)(x, y)   (2)

where y is an arbitrary Y-image height.

The aberration function given by expression (1) is calculated in advancebased on the aberration measurement result and/or simulation result.However, since it is difficult to calculate the value of expression (1)for an arbitrary divided area n, arbitrary effective light source shapeI, and arbitrary image height x, expression (1) may be determined byappropriately interpolating using the values calculated for severalvalues each of n, I, and x.

Letting x_(0n) be the image height at the center of divided area n, theaberration function in expression (1) may be substituted by:

f_(n) ^(I,C)(x)→F^(I,C)(x, x_(0n))   (3)

so that the aberration function F^(I,C)(x,x_(0n)) is used for alldivided areas 1 to 8.

The amount of variation in the aberration C due to the influence of eachdivided area under specific exposure conditions can be calculated bymultiplying the function in expression (1) by the weighting coefficientλ_(n). This calculation is valid because the weighting coefficient Ancorresponds to the amount of light which enters divided area n under theexposure conditions, and the amount of aberration variation isproportional to the amount of incident light as is commonly known.Assume, for example, that the image height coordinate position topredict a variation in focus is (0.0), the effective light source shapeunder the exposure conditions is I, the number of divided areas is 8,and the weighting coefficient in each divided area is λ_(n). Then, theamount of variation in aberration due to the influence of each dividedarea can be expressed by:

λ₁×f₁ ^(I,Focus)(0.0), λ₂×f₂ ^(I,Focus)(0.0)), . . . , λ₈×f₈^(I,Focus)(0.0)

A variation in aberration under the exposure conditions is calculated asthe sum of variations in aberrations due to the influence of the dividedareas. In the above-described example, the correction coefficient of avariation in focus at the image height coordinate position (0.0) underthe exposure conditions is given by:

$\begin{matrix}{{K^{Focus}(0.0)} = {\sum\limits_{n = 1}^{8}{\lambda_{n}{f_{n}^{I,{Focus}}(0.0)}}}} & (4)\end{matrix}$

which corresponds to K in equation (1).

The correction coefficient K can be calculated based on information onat least one of the light intensity distribution on the pupil plane ofthe projection optical system, the scanning speed, and the exposuretime, in addition to the pattern transmittance distribution informationand exposure area information.

These processing operations are performed for a combination of thenumber of image height coordinate positions to be corrected and that ofaberrations to be corrected, thereby calculating the correctioncoefficient for each image height and aberration.

A correction coefficient commonly used in a plurality of exposureconditions can be calculated by weighting correction coefficients underthe respective exposure conditions by the irradiation time (or thedimension of the exposure area in the Y direction/scanning speed), asshown in FIG. 12. In this case, the correction coefficient K used in twosets of exposure conditions is the weighted average of the correctioncoefficients K1 and K2, which are calculated under the respective setsof exposure conditions, by the irradiation time.

A second process of, when the current exposure conditions are changed,reading out a correction coefficient according to this change andcalculating and predicting the amount of aberration variation under theexposure conditions at an arbitrary image height will be explained. Asecond calculator of the main controller 103 calculates the amount ofvariation in aberration as an imaging characteristic of the projectionoptical system based on the calculated correction coefficient andexposure conditions.

The calculation for predicting a variation in the aberration of theprojection optical system is done at one or more image heights. Thecalculation of a variation in the aberration of the projection opticalsystem includes the calculation of the exposure time (Heating) andnon-exposure time (Cooling). The former is calculated by equation (2),while the latter is calculated by equation (3).

The F1 value used in equation (2) is calculated using the correctioncoefficient K calculated in the first process. The correctioncoefficient K is calculated for each image height and aberration in thefirst process.

The parameter Q in equation (1) includes one of, e.g., the exposuretime, amount of exposure, and scanning speed. The F1 value can becalculated by combining the parameter Q with the correction coefficient.In this embodiment, a value common to a plurality of image heights isused as the parameter Q.

FIG. 13 shows the state in which the F1 value changes for each imageheight because, even for the same aberration (e.g., the focus), theexposure area or mask pattern density changes and so the correctioncoefficient K changes. In this embodiment, variations in aberration arecalculated at nine image heights.

FIG. 14 illustrates an exposure sequence. The second calculator readsout a correction coefficient matching the current exposure conditions instep 1, and performs exposure processing in step 2. If the exposureconditions (e.g., the exposure amount and exposure area) for which thecorrection coefficient is calculated are different from those underwhich exposure is actually performed, a prediction error is generated inthe aberration equation. In step 3, the second calculator corrects theerror. Then, a correction coefficient best suited to the actual exposureconditions is set. In step 4, the second calculator calculates theaberration using the correction coefficient.

The second calculator calculates the maximum amount of variation (F1)for each image height from the correction coefficient calculated foreach exposure condition and the actual exposure conditions (Q). Aftercalculating the F1 value, the second calculator can predict the timecharacteristic of the amount of aberration variation ΔF by the Heatingcalculation and Cooling calculation in equations (2) and (3).

A method of correcting the amount of aberration variation calculated byaberration calculation at each image height will be explained. In thesecond process, the second calculator predicts the amount of aberrationvariation at each image height from the actual exposure conditions andthe correction coefficient calculated in the first process, andcalculates the position of a correction system so as to correct theamount of aberration variation. The projection optical system and adriving system which drives a stage such as the substrate stageconstitute the correction system. The controller controls the correctionsystem so as to reduce the amount of aberration variation calculated bythe second calculator.

To calculate the position of the correction system so as to image anoptimal pattern under the exposure conditions (e.g., the exposure areaand exposure center), a method of averagely calculating aberrationgenerated in the exposure area as shown in FIG. 15 is available. It isalso possible to calculate the position of the correction system bypredicting the amount of variation of an arbitrary aberration at anarbitrary image height based on aberration variation model simulation ata plurality of image heights, and weighting the variation in thearbitrary aberration at the arbitrary image height, as shown in FIG. 16.Although not shown, it is also possible to calculate the position of thecorrection system by predicting the amount of variation of an arbitraryaberration at an arbitrary image height based on aberration variationmodel simulation at a plurality of image heights, and weighting thevariation in the arbitrary aberration.

The position of the correction system immediately before exposure iscalculated by taking account of the influence of the pressure of anambient gas surrounding the projection optical system on the imagingprojection system from the output from a pressure sensor, and the offsetamount set to an exposure parameter or apparatus parameter.

A method of driving the correction system to the calculated position bythe controller will be explained. The projection optical systemaccording to this embodiment mounts optical element drivers whichaccurately drive optical elements such as a lens and mirror in desireddirections, in order to more precisely image a mask pattern.

FIG. 17 shows an optical system driver inserted in the projectionoptical system according to this embodiment. These driving systems adoptthe driving scheme disclosed in Japanese Patent Laid-Open No.2007-206643. This driving scheme can drive the optical elements indesired directions. For example, 17 a in FIG. 17 is a plan view of theoptical system driver in which a lens and lens frame are detached. 17 bin FIG. 17 is a plan view of the optical system driver in which the lensand lens frame are attached. 17 c in FIG. 17 is a sectional view of theoptical system driver. Referring to FIG. 17, a stationary lens barrel201 comprises a bottom surface flat portion 201 a for fixing opticalelement drivers 210 and lens position detectors 202, and a side wallcylindrical portion 201 b to connect to other vertically adjacent lensunits.

The optical element drivers 210 are formed from three identical drivingmechanisms and are arranged on the bottom surface flat portion 201 a ofthe stationary lens barrel 201. The lens position detector 202 detectsdisplacements of the lens frame in its optical axis direction and itsradial direction perpendicular to the optical axis. In accordance withthe required detection accuracy, the lens position detector 202 isappropriately selected from, e.g., an interferometric measuring unitusing a semiconductor laser, a capacitance displacement gauge, a linearencoder, and a differential transformer displacement gauge.

17 b in FIG. 17 shows the state in which the lens and lens frame aremounted. A lens frame 204 which accommodates a lens 203 has projectingflange portions at six portions on its upper surface. Three of theseflange portions are connected to displacement output portions of theoptical element drivers 210 using lens frame attaching screws 205.

A laser interferometric displacement sensor is used as the lens positiondetector 202, as will be explained with reference to 17 c in FIG. 17.For example, detection laser beams are projected onto the lens 203 inits optical axis direction and radial direction. Based on information oninterference between the reflected light beams, displacements of thelens frame 204 in its optical axis direction (Z direction) and radialdirection are detected at the three points (the vicinities of the flangeportions). With the above-described arrangement, the lens 203 can betranslated in the optical axis direction, i.e., the Z-axis directionshown in 17 c in FIG. 17 as the three optical element drivers 210 aredriven by equal amounts.

Differentiating the driving amounts of the three optical element drivers210 by a predetermined amount allows the tilt driving in the θa and θbdirections shown in 17 b in FIG. 17. The translational and tilt drivingamounts of the lens 203 can be precisely controlled by feeding back theoutput in the optical axis direction from the lens position detector 202to these driving amounts. The amount of shift in an image on a planeperpendicular to the optical axis of the lens 203 upon paralleldecentering is calculated by monitoring the output in the radialdirection from the lens position detector 202.

The driving amount of, e.g., the wafer stage is determined by takingaccount of this calculation result so that any alignment error of a maskimage upon lens decentering is eliminated. The above-described driversof the projection optical system can tilt-drive the optical elements andcan correct any aberrations by driving the optical elements in the Zdirection. This makes it possible to correct, e.g., variations inaberration which are asymmetrical about the optical axis. To correct,e.g., the focus, a correction method by driving, in the Z direction, notonly the projection optical system but also the driving unit (maskstage) which mounts the mask or the driving unit (wafer stage) whichmounts the wafer or by tilt-driving them is also available.

Second Embodiment

An embodiment when the above-described aberration correction method isapplied to a step & repeat exposure apparatus will be explained nextwith reference to FIG. 5. Since the step & repeat exposure apparatusdoes not scan a mask with a laser beam (illumination area), theillumination area on the mask is identical to the exposure area. Steps 1and 2 in FIG. 5 are the same as those in the first embodiment.

Step 3 will be explained. As the first calculation processing procedure,the illumination area is divided into a plurality of areas in the Xdirection and/or Y direction, and the mask transmittances in therespective divided areas are individually calculated. In thisembodiment, the dimension of the illumination area in the X direction is26 mm (a value when converting the dimension of the illumination area inthe X direction on the mask into that on the wafer), and the dimensionof the illumination area in the Y direction is 33 mm (a value whenconverting the dimension of the illumination area in the Y direction onthe mask into that on the wafer). Although this embodiment willexemplify a case in which the illumination area is divided into 4rectangular areas in the X direction and 4 rectangular areas in the Ydirection, i.e., a total of 16 rectangular areas, it may be divided byanother method and the shape of each divided area is not particularlylimited to a rectangle.

The mask transmittance in the divided area (to be referred to as dividedarea n; n is the area number that is one of 1 to 16 in this embodiment)is calculated as the average of transmittance data in a mask areaincluded in division area n by:

(the mask transmittance in divided area n)=(Σ transmittance data)/(thenumber of data points)

(Note that the Σ range is defined as only a mask area included individed area n)

In step 4, the mask transmittance in divided area n is normalized, and amask transmittance r_(n) in each divided area is calculated.

In steps 5 and 6, an exposure area ratio g_(n) of divided area n iscalculated based on exposure area information. The exposure areainformation herein includes dimensions wx and wy of the exposure area inthe X and Y directions, respectively, and an X-image height x₀ andY-image height y₀ at the center of the exposure area. These pieces ofinformation can be substituted by X-coordinates xr and x1 at the twoends of the exposure area in the X direction, and Y-coordinates yu andyd at the two ends of the exposure area in the Y direction.

The g_(n) value is given as the area ratio between divided area n and aportion in divided area n, which is included in the illumination areaunder a certain set of exposure conditions. That is, the g_(n) value canbe calculated on a case-by-case basis as follows:

A case in which divided area n is included in the illumination area:g_(n)=1

A case in which divided area n is not included in the illumination area:g_(n)=0

A case in which divided area n is partially included in the illuminationarea: g_(n)=((the ratio of a portion in divided area n, which isincluded in the illumination area)/(the area of divided area n))

In step 7, the weighting coefficient is calculated for each dividedarea. Let λ_(n) be the weighting coefficient calculated by multiplyingthe r_(n) value calculated from the mask transmittance by the g_(n)value calculated from the exposure area information. Then, thecoefficient λ_(n) corresponds to a value obtained by normalizing theamount of light energy which propagates through divided area n. Steps 3to 7 are repeated for each divided area n, and the weighting coefficientλ_(n) in each divided area n is calculated and stored.

Using the calculated weighting coefficient λ_(n) for each divided area,an aberration function given by expression (2) is weighted, where n isthe divided area number, I is the effective light source shape on thepupil plane, C is the type of aberration, and x and y are arbitrary X-and Y-image heights. Expression (2) represents the degree of influenceof the mask transmittance and exposure area on the aberration C as animaging characteristic, which is generated by the projection opticalsystem when divided area n is exposed with the effective light sourceshape I by the unit exposure amount, as a function of the image height(x,y). The image height (x,y) is not particularly limited to imageheights inside divided area n. This means that the light which entersdivided area n can change the aberration not only at image heightsinside divided area n but also at image heights outside divided area n.The aberration expression and its coefficients generally differ for eachaberration C and can be, e.g., a focus expression or image shiftexpression. In general, the coefficients also differ for each effectivelight source shape I. In this embodiment, an appropriate function isselected based on the effective light source information read out instep 1.

The aberration function given by expression (2) is calculated in advancebased on the aberration measurement result and/or simulation result.However, since it is difficult to calculate the value of expression (2)for an arbitrary divided area n, arbitrary effective light source shapeI, and arbitrary image height (x,y), expression (2) may be determined byappropriately interpolating using the values calculated for severalvalues each of n, I, and x.

Letting (x_(0n),y_(0n)) be the image height at the center of dividedarea n, the aberration function in expression (2) may be substituted by:

f_(n) ^(I,C)(x, y)→F^(I,C)(x, x_(0n), y, y_(0n))   (5)

so that the aberration function F^(I,C)(x,x_(0n),y,y_(0n)) is used forall divided areas 1 to 16.

The amount of aberration generation due to the influence of each dividedarea under specific exposure conditions can be calculated by multiplyingthe function in expression (2) by the weighting coefficient λ_(n). Thiscalculation is valid because the weighting coefficient λ_(n) correspondsto the amount of light which enters divided area n under the exposureconditions, and the amount of aberration generation is proportional tothe amount of incident light as is commonly known.

The sum of the amounts of aberration generation due to the influence ofthe divided areas is the amount of aberration generation under theexposure conditions. In the above-described example, the correctioncoefficient of a variation in focus at the image height coordinateposition (0.0,0.0) under the exposure conditions is given by:

$\begin{matrix}{{K^{Focus}\left( {0.0,0.0} \right)} = {\sum\limits_{n = 1}^{16}{\lambda_{n}{f_{n}^{I,{Focus}}\left( {0.0,0.0} \right)}}}} & (6)\end{matrix}$

which corresponds to K in equation (1).

These processing operations are performed for a combination of thenumber of image height coordinate positions to be corrected and that ofaberrations to be corrected, thereby calculating the correctioncoefficient for each image height and aberration.

Third Embodiment

In this embodiment, the mask transmittances at a plurality of imageheights are combined to be used as a mask transmittance at an arbitraryimage height, as shown in FIG. 18. In this case, the average of aplurality of image heights can be used or the weighted average of aplurality of image heights by the exposure area can be calculated.

Assume that the aberration variation expression calculated at anarbitrary image height in equation (1) is substituted by:

ΔF=K×T/T0×Q   (4)

where T is the mask transmittance, and T0 is a normalized masktransmittance.

Even in this case, it is possible to predict a variation in aberrationdue to a difference in mask pattern density at an arbitrary imageheight.

The mask transmittance at an arbitrary image height is calculated frommask transmittance information. Substituting the calculated value inequation (4) yields ΔF. When a variation in arbitrary aberration at anarbitrary image height is calculated from the actual exposure energyconditions, exposure time, and non-exposure time, it is possible topredict the variation in arbitrary aberration at the arbitrary imageheight.

As has been described in the first embodiment, there are a method ofcorrecting a predicted variation in arbitrary aberration at an arbitraryimage height by driving an optical element in, e.g., a projectionoptical system in the Z direction or tilt direction, and a method ofcorrecting it by driving a mask stage or wafer stage.

Devices (e.g., a semiconductor device and liquid crystal display device)are manufactured by a step of exposing a substrate coated with aphotosensitive agent to radiant energy using the above-describedexposure apparatus, a step of developing the photosensitive agent on thesubstrate exposed in the exposing step, and other known steps.

While the present invention has been described with reference toexemplary embodiments, it is to be understood that the invention is notlimited to the disclosed exemplary embodiments. The scope of thefollowing claims is to be accorded the broadest interpretation so as toencompass all such modifications and equivalent structures andfunctions.

This application claims the benefit of Japanese Patent Application No.2007-165312, filed Jun. 22, 2007, which is hereby incorporated byreference herein in its entirety.

1. An exposure apparatus comprising: an illumination optical systemconfigured to illuminate an illumination area on an original with lightfrom a light source; a projection optical system configured to project apattern of the original onto a substrate; a first stage configured tohold the original; a second stage configured to hold the substrate; anda controller configured to control driving of at least one of said firststage, said second stage, and an optical element which forms saidprojection optical system so as to reduce variations in imagingcharacteristics of said projection optical system, based on a dependenceof a transmittance of the pattern on a position in the illuminationarea.
 2. The apparatus according to claim 1, wherein said exposureapparatus includes a scanning exposure apparatus, and said controllercontrols the driving of said at least one of said first stage, saidsecond stage, and said optical element based on a dependence of thetransmittance of the pattern on a position in a direction perpendicularto a scanning direction.
 3. The apparatus according to claim 1, whereinsaid controller controls the driving of said at least one of said firststage, said second stage, and said optical element so as to decrease adependence of the variations in the imaging characteristics of saidprojection optical system on an image height, based on the dependence ofthe transmittance of the pattern on the position in the illuminationarea.
 4. The apparatus according to claim 3, wherein said controllercalculates a correction coefficient necessary for correcting thedependence of the variations in the imaging characteristics on the imageheight in accordance with the dependence of the transmittance of thepattern on the position in the illumination area, said controllercalculates a dependence of variation amounts of the imagingcharacteristics on the image height based on an exposure condition andthe calculated correction coefficient, and said controller controls thedriving of said at least one of said first stage, said second stage, andsaid optical element, based on the calculated dependence of thevariation amounts of the imaging characteristics on the image height. 5.The apparatus according to claim 4, wherein said controller calculatesthe correction coefficient based on information on a distribution of thetransmittance of the pattern in the original and information on anexposure area on the original.
 6. The apparatus according to claim 5,wherein said controller calculates the correction coefficient bymultiplying, for each of a plurality of areas obtained by dividing theillumination area, a degree of influence on the imaging characteristicsby a weighting coefficient calculated from the information on thedistribution of the transmittance and the information on the exposurearea.
 7. The apparatus according to claim 6, wherein the degree ofinfluence is calculated based on one of a measurement result andsimulation result of the imaging characteristics.
 8. The apparatusaccording to claim 1, wherein the information on the transmittance ofthe pattern is measured by said exposure apparatus or calculated fromdesign information of the original.
 9. The apparatus according to claim4, wherein said controller calculates the correction coefficient basedon at least one piece of information of an effective light source, ascanning speed of the original, and an exposure time.
 10. The apparatusaccording to claim 2, wherein the exposure condition includes at leastone of an exposure amount, a scanning speed of the original, an exposuretime, and a non-exposure time.
 11. The apparatus according to claim 1,wherein said controller controls at least one of tilt driving anddriving in a direction parallel to an optical axis of said projectionoptical system for at least one of said first stage, said second stage,and said optical element which forms said projection optical system. 12.A method of manufacturing a device, the method comprising: exposing asubstrate to radiant energy using an exposure apparatus defined in claim1; developing the exposed substrate; and processing the developedsubstrate to manufacture the device.